Consider the initial value problem:

$y^{\text{'}\text{'}}-4y^{\text{'}}-12y=8t^2{e}^{6t}-2sin(3t)cos(t)$

$y(0)=0$

$y^{\text{'}}(0)=0$

$($a$)$ Solve this using Laplace Transforms. $(5$ points$)$

$($b$)$ Can you solve this problem using a different method? If so$,$ name that method and use it to confirm your answer above. If not, explain your reasoning. $(5$ points$)$